INSTITUTE OF PHYSICS PUBLISHING NANOTECHNOLOGY Nanotechnology 15 (2004) S504–S511 PII: S0957-4484(04)77586-8 Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders

Ralf K Heilmann1,CarlGChen,PaulTKonkola and Mark L Schattenburg

Space Nanotechnology Laboratory, Center for Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

E-mail: [email protected]

Received 8 March 2004 Published 23 July 2004 Online at stacks.iop.org/Nano/15/S504 doi:10.1088/0957-4484/15/10/002

Abstract Metrology is the science and engineering of measurement. It has played a crucial role in the industrial revolution at the milli- scale and in the semiconductor revolution at the length scale. It is often proclaimed that we are standing at the threshold of another industrial revolution, brought by the advent and maturing of nanotechnology. We argue that for nanotechnology to have a similarly revolutionary effect a metrology infrastructure at and below the nanometre scale is instrumental and has yet to be developed. This paper focuses on dimensional metrology, which concerns itself with the measurement of and its applications such as pattern placement and feature size control. We describe our efforts to developgrating- and grid-based scales with sub-nanometre accuracy over 300 mm dimensions using the nanoruler—a scanning-beam interference lithography tool. (Some figures in this article are in colour only in the electronic version)

1. Introduction cost,industrial mass production for the final phase of the sec- ond industrial revolution at the beginning of the 20th century. In today’s world many engineers, scientists, and even con- The invention of the integrated circuit (IC) by Kilby sumers take the existence of, and adherence to, precise in- andNoyce in 1958 is often named as the beginning of the dustrial standards as a given. These standards form the basis information age and the semiconductor revolution. Initially, for the interchangeability and compatibility of mechanical and the mechanical metrology infrastructure with its micrometre electrical components. However, at the beginning of the first precision and accuracy was sufficient to support IC line widths industrial revolution in the middle of the 18th century the con- which started at 200 µm. At about the same time the laser was ceptofinterchangeable parts was practically unknown. Parts invented, but it took another decade before Hewlett-Packard had to be laboriously ground to fit into an assembly. Only about produced a commercial heterodyne laser interferometer, the a century later did this concept turn into reality. Interchange- first practical tool to control stage motion with interferometry ability, in turn, was enabled by the existence and widespread and nanometre resolution. Since then the wavelength of visible dissemination of improved metrology artefacts and compara- laser has become the de facto length standard at the tors such as standardized rules and affordable pocket vernier core of the metrology infrastructure of the semiconductor calipers, accurate at the milli-inch scale and below. Still sev- industry. This allowed line widths to continue to shrink down eral decades passed before pioneers such as Henry Ford and to below 100 nm today. The interferometer also is instrumental Thomas Alva Edison introduced the developed world to low- in numerous other applications where sub-micron positional accuracy is required, such as coordinate measuring machines 1 Author to whom any correspondence should be addressed. (CMMs) and diamond turning machines.

0957-4484/04/100504+08$30.00 © 2004 IOP Publishing Ltd Printed in the UK S504 Dimensional metrology for nanometre-scale science and engineering As theseexamples of previous industrial revolutions show, turbulence, position-dependent geometric errors and several amature and economic metrology infrastructure needs to optical and electronic non-linearities [4, 5]—errors that are be in place well before the confluence of new scientific difficult to eliminate due to the nature of interferometers. discoveries, new technologies developed in laboratories, Interferometers often utilize folded and time-varying visionary ideas, and appropriate support from government can beam paths which compromise accuracy, and result in large, lead to comparable revolutionary industrial developments of bulky and expensive systems, especially when multiple degrees global scale. It has been argued before that the metrology of freedom need to be measured (six or more is not uncommon). infrastructure required for a nanotechnology-based industrial In addition, large and heavy reference mirrors must be affixed revolution is yet to be established [1]. This is in accordance to the stage, increasing its size and mass, lowering its resonance with the goals of the National Nanotechnology Initiative frequency and thus increasing vibration, and requiring larger (NNI) which has identified ‘Nanoscale Instrumentation and motors, which in turn increases heat loads. The increased Metrology’ as one of several Grand Challenge Areas that have vibration and heat compromise accuracy and lower throughput. ‘the potential to realize significant economic, governmental, We believe that DMIs are near their practical accuracy limit and societal impact’ [2]. and that new approaches need to be considered for nanoscale There is a multitude of parameters and properties (electri- manufacturing, whether in the semiconductor industry or cal, magnetic, optical, chemical, mechanical, biological, etc) elsewhere. that need to be characterized at nanometre spatial dimensions andbelow,such as composition, structure, conductivity, co- 2.2. Pattern placement ercivity, and physical dimensions, just as there is a wealth of approaches on how to measure them. In this paper we The ability to place patterns with nanometre-scale features with ∼ concentrate on dimensional metrology. In the following we 1nmaccuracy or better, often over areas tens or hundreds of briefly describe shortcomings of current dimensional metrol- in size, is of increasing importance in a number ogy and areas where these limitations already slow technolog- of high-technology applications. Similarly, the National ical progress or will do so in the near future. To help solve this Science and Technology Council states that ‘instrumentation metrology problem we propose the fabrication of large-area for precise nanometre-position control across samples of gratings and grids with sub-nanometre phase accuracy. Below dimensions will be required to realize commercial we discuss their usefulness as encoder scales with the poten- nanoscale device fabrication’ [2]. In the following we tial to replace interferometer-based metrology frames, or as describe some examples of applications that critically depend large-scale, sub-nanometre accuracy pitch standards. We have on nanometre or sub-nanometre level metrology precision or constructed a prototype grating fabrication tool based on the accuracy. idea of scanning-beam interference lithography (SBIL), called the nanoruler. It is currently capable of patterning 300 mm 2.2.1. Integrated circuit fabrication. The semiconductor diameter substrates with ∼1nmpattern placement repeatabil- industry is determined to utilize its vast expertise and ity. We describe its design and capabilities in section 4 before infrastructure in lithographic patterning to fabricate integrated summarizing in section 5. circuits with ever smaller minimum feature sizes for years to come. These ICs are built up sequentially from many layers. The lithographically transferred patterns for each layer 2. Limitations of dimensional metrology and must be overlayed precisely for proper functioning of the final affected applications chip, which requires careful alignment of wafer and mask stages.The current International Technology Roadmap for 2.1. Limitations of the displacement measuring Semiconductors [6] anticipates today’s wafer overlay tolerance interferometer of 35 nm to shrink to 7.2 nm for 450 mm diameter wafer Most modern high-precision tools that require ultimate production within 15 years. Since the required wafer overlay accuracy over distances larger than a fraction of a , metrology precision should be no worse than 10% of the such as chip lithography and metrology equipment, coordinate tolerance, sub-nanometre metrology precision is required. It measuring machines, diamond turning machines and the like, is interesting to note that when patterning takes place during depend on the displacement measuring interferometer (DMI) scanning, as is the case with most current lithography step-and- for measuring the displacement of the stage that supports the scan systems, such high precision even requires the inclusion sample or work piece. of relativistic corrections in order to interpret interferometer Commercial DMIs typically have sub-nanometre resolu- data correctly [7]. tion [3], but the practical precision and accuracy that can be achieved are usually far worse. DMIs are able to perform 2.2.2. and maskless pattern generators. Many dimensional metrology to a precision approaching 200 nm types of dimensional metrology tools with sub-micron and (0.2 µm) in an ordinary laboratory or factory environment, in some cases sub-nanometre resolution are available today. ∼10 nm in a well-controlled environment, and ∼2nmina Examples are optical and electron microscopes, and proximity vacuum chamber. While this level is sufficient for patterning probes such as scanning tunneling microscopes and atomic 100 nm features, it is insufficient for the measurement and force microscopes. Similarly useful in nanoscale science control of features under 10 nm. The primary errors plagu- and engineering are related maskless patterning tools such ing interferometers include environmental disturbances such as as electron and laser beam writers. However, in many of temperature, pressure and humidity fluctuations,atmospheric these tools the stage that holds the sample being measured

S505 RKHeilmann et al or patterned has an accuracy at least an order of magnitude Stationary Grating f f worse than the probe resolution. And since the area accessible D Mirror θ d to the probe—often called the field—is typically only a few Substrate Substrate to afew hundred microns in size, larger areas are imaged f f Stage Stage f f Optical v v D or patterned by stitching together different fields obtained by Fibre moving the sample stage. Therefore stage inaccuracies lead (a) (b) to stitching errors at the field boundaries and makeitdifficult to locate features or characterize processing-induced changes. Figure 1. Schematic comparison between (a) displacement Probe deflection non-linearities within a field cause intra-field measuring interferometry and (b) optical encoder. A laser beam of frequency f is split in two by a beam splitter. In case (a) one beam distortions and also contribute to stitching errors. A metrology traverses a variable distance to the stage, which moves with velocity frame with sub-nanometre accuracy over macroscopic length v,and is reflected back with a Doppler-shifted frequency scales could reduce stage-limited inter-field errors and serve as fD = f (1 − vn/c) before being superimposed with the stationary apitch standard to calibrate and subtract intra-field distortions. arm of frequency f .Theindex of refraction is n,andc is the The feasibility of this idea has been demonstrated for electron velocity of light in vacuum. In case (b) the beam splitter is mounted to the moving stage. It sends one beam to the stationary grating, beam writing in the form of spatial-phase-locked electron- where it is diffracted back and undergoes a frequency shift beam lithography (SPLEBL), with resulting field-stitching f = f − fD =−f (vn/c) sin θ.Itisthensuperimposed with the errors and global placement accuracy relative to a fiducial grid other arm of frequency f .Thegeometrical path lengths between of below 1.3 nm (1σ)[8]. splitting and recombining the laser beam remain constant and independent of stage translation. The distance travelled through air can be made as short as a few hundred microns or less. 2.2.3. Nanomagnetic media. Pattern placement metrology will also be crucial for the development of patterned magnetic boundaries. A possible approach to macroscopically ordered recording media. Traditional continuous thin film magnetic self-assembly might involve the use of patterned templates recording media are required to support higher and higher as substrates [12, 13]. For example, surface relief gratings bitdensities, rapidly approaching the superparamagnetic limit with a coarse period comparable to the diameter of ordered where individual grains are so small that thermal energy self-assembled domains could force molecules to assemble alone allows them to reverse magnetization spontaneously, with long-range order due to the additional, substrate-imposed rendering them useless for long-time data storage. A much constraints. For optimum control of defects it is desirable to explored alternative to achieve higher bit densities is the use place the template pattern with an accuracy of a fraction of the of media consisting of pre-patterned arrays of single-domain nearest-neighbor distance of the assembling molecules. This magnetic particles [9]. Thermally stable particles of less than can easily result in a 1 nm template accuracy requirement. 10 nm diameter are conceivable. However, in the case of spinning-disc systems synchronization between the read-and- 2.3. Coordinate measuring machines write process and the position of individual magnetic particles with a pitch of 25 nm (160 Gbits cm−2) already is predicted Coordinate measuring machines play a crucial role in almost to require pattern edge jaggedness of ∼1nmorless[10]. any kind of modern precision engineering on the macroscopic Certainly pattern placement metrology accuracy at the sub- scale. The number of applications where large scale tools and nanometre levelisdesired. parts need to be shaped, assembled, aligned and characterized with sub-micron precision and accuracy is steadily increasing. Some examples are the manufacture of large precision optical 2.2.4. Optoelectronic devices. Grating-based opto- surfaces in general, or the diamond turning of assembly electronic devices, such as Bragg grating channel add-drop tooling for x-ray optics in astronomy in particular [14], where filters, can serve as high-bandwidth optical switches [11]. sub-micron accuracy is required over volumes of the order Surface relief gratings on waveguides may be many millimetres of 1 m3.Evenmoredemanding are the requirements for long, but at the same time they require the grating lines to be extreme ultraviolet (EUV) optics that offer an avenue to take placed accurately within 5 nm or better over the whole length semiconductor device fabrication to the 30 nm feature size for optimum performance. This exceeds the capabilities of level. Assembly tolerances are in the nanometre range, and the best commercial electron beam writers. And again, the the optic figure of the order of 0.1 nm [15]. Precision CMMs underlying dimensional metrology needs to be accurate at the mostly rely on metrology frames based on laser interferometers 1nmlevel. and are therefore subject to the shortcomings discussed above (see section 2.1). 2.2.5. Templates for self-assembly. The ability of molecules to self-assemble into large and complex structures is one 3. Opticalencoders of nature’s great lessons that researchers are only beginning to utilize. Self-assembly has been employed to create Optical encoders have been used for decades as displacement many systems with sub-micron scale features, such as self- measuring devices. In simple terms, an encoder consists of a assembled monolayers on solid (SAMs) and liquid (Langmuir scale and a scanning device that reads off the scale. Optical monolayers) substrates. However, most of these systems encoder scales are rigidly attached to a metrology frame and are quasi-two-dimensional in nature, and therefore do not consist of grating or grid plates, and the read head—typically possess sufficient long-range order, but instead display mounted to a moving stage—senses displacement relative to ordered domains of limited size, separated by domain the grating scale (see figure 1). Highest resolution (a small

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(a) (b)

Substrate X Direction Optical Laser Scanning Bench Grating Image Air-Bearing X-Y Stage θ θ Interferometer Resist- coated XY Stage Direction

Y Substrate Air Bearing Granite Slab

(d) Intensity (c) Summed Intensity of Scans 1-6

Intensity Grating Period Scan Scan Scan Scan Scan Scan p=λ/(2sinθ) 1 2 3 4 5 6

X X

Figure 2. Schematic description of scanning-beam interference lithography. (a) Two Gaussian beams from a laser interfere at half-angle θ on the surface of a stage mounted substrate. The blow-up shows the standing wave interference pattern or interference fringes. (b) The whole resist-coated substrate is exposed by scanning the stage under the grating image. (c) Schematic intensity distribution within the interference region. (d) Desired dose uniformity in the resist is achieved through appropriate overlapping of subsequent scans. fraction of the grating period) is achieved with a variety of gratings of many in size with sub-nanometre diffraction-based schemes [16, 17]. The main advantages accuracy [19]. of optical encoders are the short and constant beam path lengths between gratings and sensors, reducing the effects 4.1. Scanning-beam interference lithography of the atmosphere by orders of magnitude compared to laser Over the last several years our laboratory has developed a interferometers. The use of optical encoders also allows one patterning tool with the above demands in mind. It is based to replace the heavy interferometer stage mirrors required for on the technique of scanning-beam interference lithography DMIs with miniaturized encoder sensors, thereby increasing (SBIL), which can be described as a hybrid between IL stage resonance frequency and reducing stage weight. The and mechanical ruling (see figure 2). Similar to IL, it main problem with encoders today is that commercially uses the grating-like interference pattern (‘image grating’) ∼ available encoder plates have accuracies worse than 100 nm generated at the intersection of two coherent laser beams to over centimetre length scales. Eventhebest custom made expose a resist-covered substrate. In contrast with IL, which scales are only accurate at the 100 nm level [18]. Since the often uses expanded spherical beams resulting in hyperbolic encoder can only be as accurate as the grating scale, advance in interference patterns, SBIL employs narrow, collimated beams this area crucially depends on the availability of encoder plates of only ∼1–2 mm diameter, resulting in an ultra-low-distortion with sub-nanometre accuracy over macroscopic distances [19]. image grating. Similar to mechanical ruling, the substrate is now scanned back and forth in serpentine fashion, with 4. Towards nanometre-accurate grating fabrication the interfering laser beams effectively acting as a scribe with with the nanoruler thousands of ‘tips’ that rules thousands of lines in parallel. Due to the Gaussian nature of the laser beams it is necessary Diffraction gratings are typically manufactured in one of two to overlap neighboring passes (‘scans’) sufficiently to achieve ways [20]. They are either mechanically ruled with a diamond a uniform exposure dose on the substrate. The challenge for tip, which is a very slow, expensive, and difficulttocontrol SBIL is to step over exactly by an integer multiple of the image grating period between scans, and to lock the image grating process, especially for large gratings with fine periods, or phase to the substrate reference frame during scanning in order thegrating pattern is defined lithographically—typically by to achieve straight grating lines in the resist with nanometre interference lithography (IL)orelectron beam lithography spatial phase coherence across the whole substrate. (EBL)—in a resist layer and then chemically transferred into asubstrate. IL is fast, but prone to hyperbolic distortions [21], 4.2. The nanoruler while EBL patterns suffer from high frequency jitter and stitching errors and still take considerable time to write. Today The nanoruler is an SBIL tool for the patterning and metrology neither one of these techniques is capable of producing linear of gratings in excess of 300 mm × 300 mm in size. The

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DSP/ Frequency Comparator Synthesizer DSP/ Frequency Comparator Synthesizer

AOM3

AOM2 AOM2 AOM1 AOM1

fH

PM3 PM2 PM1

f fL R f fL R

CCD PM4

Wafer Grating Stage X-Y Stage X-Y Stage Stage Control Control

(a) (b)

Figure 3. Schematics of nanoruler operational modes. (a) Writing or patterning mode: left arm (frequency fL)and right arm (frequency fR), which are both frequency shifted by 100 MHz via acousto-optic modulators AOM1 and AOM2, are partially picked off just before they interfere and combined with the diffracted output beam from AOM3, which operates at 120 MHz for heterodyning with a 20 MHz carrier frequency. The phase difference between phase meters PM1 and PM2 and the stage interferometer data are fed back into a digital comparator. The frequency synthesizer then adjusts the drive frequency for AOM1 to lock the phase of the image grating to the stage frame of reference. (b) Reading or metrology mode: a diffraction grating is taking the place of the substrate on the stage. AOM1 operates at a drive frequency of 90 MHz and AOM2 at 110 MHz. The feedback signal from phase meter PM3 and the stage interferometer are used to adjust the AOM1 frequency to generate a 20 MHz heterodyne signal at phase meter PM4, which measures the phase of the superposition of the reflected right arm and the −1order of the left arm back-diffracted from the grating. Any deviation from the 20 MHz heterodyne frequency at PM4 is equivalent to a fringe-to-substrate motion in writing mode.

‘metrology mode’ allows the mapping or ‘reading’ of the Distortions in the grating image are mapped through phase- spatial phase of existing gratings with the same accuracy as shiftinginterferometry and can be minimized through the the gratings patterned in the ‘writing mode’ (see figure 3). adjustment of spatial filter lenses in each arm [24, 25]. The nanoruler sits on top of a massive granite block, which Just before the two beams interfere at the substrate a beam in turn is supported by an active vibration isolation system splitter picks off a fraction of the incident power in each arm. with added feed forward controltocompensate for stage These beams, together with a frequency-shifted third arm for motion. On top of the granite block glides a motorized x– heterodyning, are guided through optical fibres to digital phase y airbearingstage with Zerodur mirrors and a Super Invar meters. The phase signals are used as feedback to lock out vacuum chuck. Stage position feedback is provided through a image fringe movement due to environmental disturbances. commercial heterodyne DMI system operating at a wavelength The fringe-locking optics are mounted on a single Zerodur of λ = 633 nm. metrology block, using a custom designed beam splitter and Attached to the granite block is a vertical optical bench thermally balanced mounts to minimize phase differences that holds numerous optics for interference lithography and between the image grating on the substrate and the phase metrology. The reading and writing interferometry employs measurement. The phase meter signal, together with stage aremotely operated Ar-ion laser with λ = 351.1nm.The DMI information, is fed back to a digital signal processor, period p of the image grating is given by which in turninstructs a custom digital frequency synthesizer λ that drives acousto-optic modulators in each lithography arm, p = , (1) thereby locking the image grating spatial phase to the moving 2sin(θ) substrate frame [26–28]. where θ is the half angle between the two interfering arms. The fringe-to-substrate phase placement repeatability The laser beam is locked to the frame of the optical bench is thefundamental metric in the design of our current through a beam steering system [22]. It is split into two arms prototype [28]. Error sources that reduce repeatability can with a grating beam splitter. The two arms are aligned with be grouped by subsystem (see table 1) or by their physical acomputerized alignment system to interfere at the substrate origin (see table 2). We distinguish between subsystems as at the desired angle[23]. The period of the image grating follows. The stage DMI measures the displacement of the is verified interferometrically with a precision better than sample stage with respect to the column reference mirror, 3 ppm (3σ), or 1.1 pm for a period p = 400 nm [24, 25]. which is integrated into the metrology block. Repeatability

S508 Dimensional metrology for nanometre-scale science and engineering Table 1. Error budget summary by subsystems. The ‘static’ case system and directly measure the remaining fringe-to-substrate refers to a thermally well equilibrated system with a short (<7cm) displacement (see figure 3). This is achieved by heterodyne interferometer dead path and no clamping distortions. The ‘worst measurement of the phase in the superposition of the reflected case’ scenario applies to patterning a 300 mm substrate and includes additional thermal expansion errors from moving the stage through a (zero order) beam from one arm and the diffracted (minus first thermal gradient, the longer dead path, and clamping distortions. order) beam from the other arm. We can thus directly observe the fringe-to-substrate motion under conditions equivalent to Error budget Error budget (‘static’) (‘worst case’) writing mode. Typical fringe placement errors are on the order Error category (±nm) (±nm) of 2.1 nm (3σ)[27, 28]. Probably the biggest advantage of the SBIL technique Displacement interferometer 1.66 4.88 Fringe locking interferometer 1.58 1.58 is the dose averaging that takes place in the resist due to Metrology block frame 0.51 0.51 scanning and overlapping exposures. This averaging greatly Substrate frame 0.40 2.83 reduces the effect of any remaining image grating distortions, Rigid body error motions 0.12 0.12 period measurement inaccuracies, and high-frequency fringe- rss error 2.39 5.88 to-substrate motion[24, 27, 28]. Experimentally we find grating mapping repeatability over a 100 mm diameter grating to be better than 3 nm (3σ)[27, 28]. Taking into account Table 2. Error budget summary grouped by physical origin for the the attenuation of high frequency disturbances due to the ‘worst case’ scenario as described in table 1. dose averaging over 2 mm diameter beams during scanning Error budget at 100 mm s−1,weexpect dose placement stability of 2.1 nm Error category (±nm) (3σ). Furthermore, the effects of periodic DMI errors Thermal expansion 2.46 (observed to be of the order of 0.35 nm (1σ)inour system) Air index variations 5.00 could be averaged out to a large extent simply by scanning both Periodic interferometer error 1.02 stageaxesinamanner that pushes these errors to high enough Electronic errors 0.22 Vibration 0.08 frequencies [28]. Substrate clamping distortion 1.41 We have patterned 300 mm diameter substrates with Substrate thickness variation 0.50 a 400 nm period grating in about 20 min (see figure 4). Control loop 0.40 Mechanically ruling the same grating would require a single rss error 5.88 diamond tip to travel more than 200 km, which would lead to excessive tip wear, and would take well over a month of continuous work under the best of circumstances. in this measurement is compromised by thermal expansion, So far our efforts have focused on achieving a high level air index variations, periodic interferometer errors, electronic of repeatability in the patterning of large-area gratings. We errors, and inaccuracies in refractometer correction. Errors are currently investigating repeatable systematic errors, such in theUVlithography interferometer are due to imperfections as those due to stage mirror non-flatness or interferometer in the fringe-locking sensor signal and electronics, air index misalignment, to improve system accuracy. We believe that variations, periodic UV interferometer errors, and control loop repeatability is primarily limited by remaining air index non- performance. Metrology block errors describe thermal and uniformity, thermal expansion effects, and periodic stage vibration-induced motion of fringe-locking optics relative to interferometer non-linearities (seealso table 2). Detailed error the column reference mirror. Substrate frame errors consist analysis tells us that reduced temperature gradients, wider use of changes or imperfections in substrate location with respect of lower expansion materials such as Zerodur, possible vacuum to the stage mirror, which are due to vibrations, thermal enclosure of a stage interferometer arm, and scanning strategies effects, substrate clamping distortions, and substrate non- that minimize periodic DMI errors will allow grating patterning flatness. Rigid body error motions lead to errors due to relative and mapping repeatability well under 1 nm (3σ)[28]. motions between stage, metrology block, interferometer heads, and interferometer beams, and are dominated by Abbe errors. 5. Summary and outlook The whole nanoruler is placed inside an environmental class 10 clean room enclosure that controls temperature As with past industrial revolutions, the nanotechnology ◦ fluctuations to within ±0.005 Candhumidity to within revolution depends on the existence of a capable and ±1%. The enclosure, in turn, sits inside a larger temperature economical metrology infrastructure before it can proceed controlled class 100 clean room. In addition, slow, uniform swiftly. This infrastructure is currently not in place. In the variations in the index of refraction, such as those due to area of macroscopic dimensionalmetrology the shortcomings changes in pressure, humidity, and CO2 levels, are corrected of displacement measuring interferometry can be overcome through the use of a refractometer close to the region of through the employment of optical encoder schemes that interference[27, 28]. utilize nanometre precise and accurate encoder plates. We Nevertheless, while writing we have no separate measure have introduced scanning-beam interference lithography as of inaccuracies in the stage DMI readings and small variations apromisingtechnique for the fabrication of such encoder in the short optical paths between substrate and fringe-locking plates. With the nanoruler, our prototype SBIL tool, we optics due to vibrations, distortions, and index variations. In have so far demonstrated pattern placement control and reading mode, however, where the beam paths are practically mapping repeatability better than 3 nm (3σ)andexpect further identical to writing mode, we can also utilize our fringe-locking improvement. Ultimately, the DMI-based stage control itself

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Resist

400 nm

ARC

Silicon (a) (b)

Figure 4. (a) A 300 cm diameter silicon wafer patterned in the nanoruler with a 400 nm period grating. Overhead fluorescent lighting and the camera flash diffract off the grating. (b) Scanning electron micrograph of a resist grating on an anti-reflection coated (ARC) silicon wafer after exposure in the nanoruler and development. will be replaced by accurate, stable, calibrated encoders [7] Heilmann R K, Konkola P T, Chen C G and that allow traceability to length standards. In the future, Schattenburg M L 2000 J. Vac. Sci. Technol. B 18 3277 encoder grids (i.e. two orthogonal gratings for metrology [8] Smith H I, Hector S D, Schattenburg M L and Anderson E H 1991 J. Vac. Sci. Technol. B 9 2992 in twodimensions) can be patterned either through double ◦ Hastings J T, Zhang F and Smith H I 2003 J. Vac. Sci. Technol. exposure of a substrate with exact 90 substrate rotation B 21 2650 between exposures, or through extension of the current system [9] Ross C A 2001 Annu. Rev. Mater. Res. 31 203 from two to four interfering beams. As we have demonstrated, [10] Nair S K and New R M H 1998 IEEE Trans. Magn. 34 1916 large-area encoder plates can be patterned in less than an [11] Lim M H, Murphy T E, Ferrera J, Damask J N and Smith H I 1999 J. Vac. Sci. Technol. B 17 3208 hour, which holds the promise of inexpensive high-volume [12] Cheng J Y, Ross C A, Thomas E L, Smith H I and production. In addition various methods of grating or grid Vancso G J 2003 Adv. Mater. 15 1599 replication could lower the price of such encoder plates even [13] Segalman R A, Hexemer A and Kramer E J 2003 more, assuming the replication process can be controlled well Macromolecules 36 6831 [14] Podgorski W A et al 2004 Optics for EUV, x-ray, and enough to keep distortions at the sub-nanometre level over all gamma-ray astronomy Proc. SPIE 5168 318 relevant length scales. Furthermore we believe that it will be Owens S M, Hair J, Stewart J, Petre R, Zhang W, possible to add the ability to vary the period and orientation of Podgorski W, Glenn P, Content D, Saha T and the image grating during scanning [29] to generate accurately Nanan G 2004 Proc. SPIE 5168 239 chirped or curved gratings for applications in spectroscopy and [15] Goldberg K A, Naulleau P, Batson P, Denham P, Anderson E H, Chapman H and Bokor J 2000 J. Vac. Sci. optoelectronic devices. Technol. B 18 2911 [16] Teimel A 1992 Prec. Eng. 14 147 Acknowledgments [17] Jourlin Y, Jay Y and Parriaux O 2002 Prec. Eng. 26 1 [18] Bosse H, Hassler-Grohne¨ W, Flugge¨ J and Koning¨ R 2003 Recent developments in traceable dimensional We are grateful for the outstanding technical and facility measurements II Proc. SPIE 5190 122 support from R C Fleming, the Space Nanotechnology Bosse H, Hassler-Grohne¨ W, Flugge¨ J and Koning¨ R 2003 Laboratory, and the Nanostructures Laboratory. The 300 mm Metrologia 40 04002 (Techn. Suppl.) diameter gratings were patterned by J C Montoya. RKH [19] Schattenburg M L, Chen C, Everett P N, Ferrera J, acknowledges helpful conversations with T W Zeiler. This Konkola P and Smith H I 1999 J. Vac. Sci. Technol. B 17 2692 work was supported through grants from NASA and DARPA. [20] Loewen E G and Popov E 1997 Diffraction Gratings and Applications (New York: Dekker) References [21] Ferrera J, Schattenburg M L and Smith H I 1996 J. Vac. Sci. Technol. B 14 4009 [1] Schattenburg M L and Smith H I 2001 Nanostructure science, [22] Konkola P T, Chen C G, Heilmann R K and metrology, and technology Proc. SPIE 4608 116 Schattenburg M L 2000 J. Vac. Sci. Technol. B 18 3282 [2] National Nanotechnology Initiative 2004 Research and [23] Chen C G, Heilmann R K, Joo C, Konkola P T, Pati G S and development supporting the next industrial revolution Schattenburg M L 2002 J. Vac. Sci. Technol. B 20 3071 supplement to the President’s FY budget, National Science [24] Chen C G 2003 Beam alignment and image metrology for and Technology Council scanning-beam interference lithography—fabricating http://www.ostp.gov/NTSC/html/NTSC Home.html gratings with nanometer phase accuracy PhD Thesis [3] Demarest F C 1998 Meas. Sci. Technol. 9 1024 Department of Electrical Engineering and Computer [4] Bobroff N 1993 Meas. Sci. Technol. 4 907 Science, Massachusetts Institute of Technology, Cambridge, [5] Teague E C 1993 SPIE Institutes for Advanced Optical MA Technologies Series IS-10 ed C Marrion (Bellingham, WA: http://snl.mit.edu/papers/theses/2003/cgc phd thesis.pdf SPIE Optical Engineering Press) p 322 and http://theses.mit.edu/ [6] International Technology Roadmap for Semiconductors [25] Chen C G, Konkola P T, Heilmann R K, Joo C and http://public.itrs.net/ Schattenburg M L 2002 Nano- and microtechnology:

S510 Dimensional metrology for nanometre-scale science and engineering materials, processes, packaging, and systems Proc. SPIE Mechanical Engineering, Massachusetts Institute of 4936 126 Technology, Cambridge, MA [26] Heilmann R K, Konkola P T, Chen C G, Pati G S and http://snl.mit.edu/papers/theses/2003/ptk-phdthesis.pdf and Schattenburg M L 2001 J. Vac. Sci. Technol. B http://theses.mit.edu/ 19 2342 [29] Schattenburg M L, Chen C G, Heilmann R K, Konkola P T and [27] Konkola P T, Chen C G, Heilmann R K, Joo C, Montoya J C, Pati G S 2002 Optical spectroscopic techniques and Chang C-H and Schattenburg M L 2003 J. Vac. Sci. instrumentation for atmospheric and space research IV Technol. B 21 3097 Proc. SPIE 4485 378 [28] Konkola P T 2003 Design and analysis of a scanning-beam Pati G S, Heilmann R K, Konkola P T, Joo C, Chen C G, interference lithography system for patterning gratings with Murphy E and Schattenburg M L 2002 J. Vac. Sci. Technol. nanometer-level distortions PhD Thesis Department of B 20 2617

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